Define indexing

[ChrisRackauckas]

You should define getindex operations so that way indexing works.

[ChrisRackauckas]

Indexing should also automatically give + and -. Though you may want specific fast overloads for standard + and - operations.

[shivin9]

Indexing should also automatically give + and -. Though you may want specific fast overloads for standard + and - operations.

Can you explain that comprehensively? Do you mean to add operators to form a sort of composed PDE operator as in LinearMaps?

[ChrisRackauckas]

Lazy composed PDE operators is another thing that's needed, but that should be a separate issue.

Just simple + and - vs AbstractMatrices would be nice, because then you could L + M for any sparse matrix directly without producing a temporary like sparse_full(L) + M. Setting up indexing will make this just work, but you can make it better by setting it up to only loop through the bands. This gives you a way to then compose these even when not every operator can be of this special form.

[shivin9]

Some indexing support has also been pushed here.

[shivin9]

well there you go

julia> A = LinearOperator{Float64}(2,2,8);
julia> m = ones(8,8);
julia> res = A+m
LinearMaps.LinearCombination{Float64,Tuple{PDEOperators.LinearOperator{Float64,StaticArrays.SVector{3,Float64}},LinearMaps.WrappedMap{Float64,Array{Float64,2}}},Tuple{Float64,Float64}}((PDEOperators.LinearOperator{Float64,StaticArrays.SVector{3,Float64}}(2,2,8,3,[1.0,-2.0,1.0],3,4),LinearMaps.WrappedMap{Float64,Array{Float64,2}}([1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0; … ; 1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0],true,true,true,false)),(1.0,1.0))

julia> full(res)
8×8 Array{Float64,2}:
 -1.0   2.0   1.0   1.0   1.0   1.0   1.0   1.0
  2.0  -1.0   2.0   1.0   1.0   1.0   1.0   1.0
  1.0   2.0  -1.0   2.0   1.0   1.0   1.0   1.0
  1.0   1.0   2.0  -1.0   2.0   1.0   1.0   1.0
  1.0   1.0   1.0   2.0  -1.0   2.0   1.0   1.0
  1.0   1.0   1.0   1.0   2.0  -1.0   2.0   1.0
  1.0   1.0   1.0   1.0   1.0   2.0  -1.0   2.0
  1.0   1.0   1.0   1.0   1.0   1.0   2.0  -1.0

This "just works" property is too good.